1. Field of the Invention
This invention relates to a neural network architecture having phase-coherent alternating current neuron input signals, that are combined by capacitive coupling to give a weighted sum signal, which is then rectified and further non-linearly processed to yield the neuron output.
2. Description of the Related Art
Electrical networks and optical analogs having neuron-like properties have been widely studied in recent years, with the aim of solving problems such as pattern recognition, associative memory, and combinatorial optimization, which are difficult to deal with by conventional computational approaches. Extensive theoretical work on neural networks has also been pursued, and good summaries of the current status of the subject can be found in the recent books: Wasserman, P. D., Neural Computing, Theory and Practice, Van Nostrand Reinhold, 1989, and Hertz, J., Krogh, A., and Palmer, R. G., Introduction to the Theory of Neural Computation, Addison-Wesley, 1991. The basic computational element, or neuron, in the prior art described in these references is the Mc Culloch-Pitts neuron, represented by the equation ##EQU4## in which v.sub.k.sup.in and v.sub.i.sup.out are respectively inputs and outputs which take the values 0 or 1, w.sub.ik and t.sub.i are respectively weights and a threshold which can take any real number values, and .theta. is the Heaviside step function defined by ##EQU5## In some applications, the neuron is alternatively defined by ##EQU6## with the inputs and outputs now taking the values -1 or 1, and with .epsilon. the function defined by ##EQU7## The functions .theta.(x) and .epsilon.(x) can both be considered as special cases of a more general step function which takes the value -.lambda., with .lambda. any positive number, for x&lt;0, and which takes the value 1 for x.gtoreq.0; .theta. and .epsilon. then correspond, respectively, to the cases .lambda.=0 and .lambda.=1. In certain applications, and particularly for network training, the discontinuous functions .theta.(x) and .epsilon.(x) are replaced by continuous "sigmoidal" or "squashing" functions which vary continuously between the respective limits 0,1 or -1, 1 as x crosses a narrow band around x=0; this fact should be kept in mind but does not affect the ensuing discussion in any significant way. Mc Culloch-Pitts neurons can be configured in layered "feed-forward" networks, in which the outputs of neurons at a given layer are fed into the inputs of the neurons of the next layer, as in the basic "perceptron" described in U.S. Pat. No. 3,287,649 to Rosenblatt. Alternatively, the neurons can be configured in "recurrent" networks, in which the outputs of a layer are fed back into the inputs of the same layer, as in the networks described in U.S. Pat. No. 4,660,166 to Hopfield and U.S. Pat. No. 4,719,591 to Hopfield and Tank.
Although representing a potentially powerful new computational method, neural networks of the prior art suffer from a number of limitations, which we now describe.
1. Computational Limitations: Networks based on the Mc Culloch-Pitts neuron have some well-known computational limitations. (See Wasserman, op. cit., pages 30-36, and Hertz, Krogh and Palmer, op. cit., pages 96-97 and 130-131.) For example, a single layer perceptron cannot solve the problem of representing the "Exclusive Or" (XOR) function, EQU v.sup.out =XOR(v.sub.1.sup.in, v.sub.2.sup.in), (5)
with the function XOR defined by the truth table ##EQU8## The reason the Mc Culloch-Pitts neuron cannot represent XOR is simply illustrated by considering a sum variable S defined by S=v.sub.1.sup.in +v.sub.2.sup.in. To compute XOR as a function of S one need a function which gives 0 when S=0, which gives 1 when S=1, but which again gives 0 when S=2, corresponding respectively to the cases of 0, 1 or 2 inputs in the "on" state. This computation cannot be performed by a linear thresholding device, which can only do the computation of giving an output 0 when S is less than some value T, and an output of 1 when S is larger than T. In other words, as the variable S increases, the Mc Culloch-Pitts neuron can only switch once from "off" to "on", whereas to compute XOR one needs a neuron which can switch from "off" to "on", and then back to "off" again. To represent XOR using Mc Culloch-Pitts neurons, one needs at least a two-layer neural network.
A second computational limitation of networks based on the Mc Culloch-Pitts neuron has to do with convexity properties. A convex set n-dimensional space is a set with the property that if one picks any two points on the boundary, the straight line segment joining these points lies entirely within the set. In three dimensional space, a sphere is convex, and a cube is convex, but a bowl-shaped object is not convex. Returning now to neural nets, a standard result in perceptron theory states that a one- or two-layer perceptron can only select for input vectors (v.sub.1.sup.in, . . . , v.sub.n.sup.in) lying in a convex region in n-dimensional space; one must go to at least three-layer perceptrons to select for non-convex regions.
2. Power dissipation in the voltage divider: Prior art patents (see, e.g. U.S. Pat. No. 4,660,166 to Hopfield) use a pair of complementary negative and positive voltage neuronal output lines to realize weights of both signs; to get a positive (negative) synaptic matrix weight, a resistive voltage divider is connected respectively to the positive (negative) line. In this realization of the synaptic matrix, power dissipation in the resistors imposes an important limitation on designing very large scale integrated neural network circuits. It would thus be desirable to have a non-dissipative realization of the weights, and a number of ideas have been suggested in the prior art to try to achieve this. Coherent optical neurons have been suggested which realize the weights in non-dissipative fashion as volume holograms in photorefractive crystals, and which can potentially give a very high synaptic density; see especially Psaltis, Brady and Wagner, "Adaptive optical networks using photorefractive crystals", Applied Optics Vol. 27, No. 9, May 1, 1988, pages 1752-1759, and an improvement on the method of the Psaltis et al. article disclosed in U.S. Pat. No. 4,959,532 to Owechko. The methods of both of these prior-art references suffer from the disadvantage of requiring very critical mechanical alignment in order to achieve the necessary coherence, which will make it hard to achieve eventual miniaturization and mass production. In electronic circuit technology, a realization of the neural weights by capacitors, which is non-dissipative and has other advantages as well, has been described by Cilingiroglu, "A Purely Capacitive Synaptic Matrix for Fixed-Weight Neural Networks", IEEE Transactions on Circuits and Systems, Vol. 38, No. 2, February 1991, pages 210-217. The method of this prior-art reference has appealing features, but requires an elaborate clocking scheme with three clock phases, corresponding to precharge, evaluation and output switching states of the capacitive network. Similar clocking requirements are inherent in two earlier switched-capacitor neural network methods, described in Tsividis and Anastassiou, "Switched-Capacitor Neural Networks", Electronics Letters Vol. 23, No. 18, August 1987, pages 958-959, and in Horio, Nakamura, Miyasaka and Takase, "Speech Recognition Network With SC Neuron-Like Components", Proceedings of the 1988 IEEE International Symposium on Circuits and Systems, Vol. 1, pages 495-498.